### Abstract

We prove a law of large numbers in terms of uniform complete convergence of independent random variables taking values in functions of 2 parameters which share similar monotonicity properties as the increments of monotone functions in the initial and the final time parameters. The assumptions for the main result are the Holder continuity on the expectations as well as moment conditions, while the sample functions may contain jumps.

Original language | English |
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Pages (from-to) | 171-192 |

Number of pages | 22 |

Journal | Journal of Mathematical Sciences (Japan) |

Volume | 25 |

Issue number | 2 |

Publication status | Published - 2018 Jan 1 |

### Fingerprint

### Keywords

- Complete convergence
- Counting process
- Law of large numbers
- Sum of independent random processes

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Doubly uniform complete law of large numbers for independent point processes.** / Hattori, Tetsuya.

Research output: Contribution to journal › Article

*Journal of Mathematical Sciences (Japan)*, vol. 25, no. 2, pp. 171-192.

}

TY - JOUR

T1 - Doubly uniform complete law of large numbers for independent point processes

AU - Hattori, Tetsuya

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We prove a law of large numbers in terms of uniform complete convergence of independent random variables taking values in functions of 2 parameters which share similar monotonicity properties as the increments of monotone functions in the initial and the final time parameters. The assumptions for the main result are the Holder continuity on the expectations as well as moment conditions, while the sample functions may contain jumps.

AB - We prove a law of large numbers in terms of uniform complete convergence of independent random variables taking values in functions of 2 parameters which share similar monotonicity properties as the increments of monotone functions in the initial and the final time parameters. The assumptions for the main result are the Holder continuity on the expectations as well as moment conditions, while the sample functions may contain jumps.

KW - Complete convergence

KW - Counting process

KW - Law of large numbers

KW - Sum of independent random processes

UR - http://www.scopus.com/inward/record.url?scp=85054836351&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85054836351&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85054836351

VL - 25

SP - 171

EP - 192

JO - Journal of Mathematical Sciences (Japan)

JF - Journal of Mathematical Sciences (Japan)

SN - 1340-5705

IS - 2

ER -